Optical metrology techniques generally referred to as scatterometry offer the potential to characterize parameters of a workpiece (i.e., a sample) during a manufacturing process. In practice, light is directed onto a periodic grating formed in a workpiece and spectra of reflected light are measured and analyzed to characterize the grating. Characterization parameters may include critical dimensions (CDs), sidewall angles (SWAs) and heights (HTs) of gratings, material dispersion parameters, and other parameters that affect the polarization and intensity of the light reflected from or transmitted through a material. Characterization of the grating may thereby characterize the workpiece as well as the manufacturing process employed in the formation of the grating and the workpiece.
For example, the optical metrology system 100 depicted in FIG. 1 can be used to determine the profile of a grating 102 formed on a semiconductor wafer 104. The grating 102 can be formed in test areas on the wafer 104, such as adjacent to a device formed on the wafer 104. The optical metrology system 100 can include a photometric device with a source 106 and a detector 112. The optical metrology system 100 illuminates the grating 102 with an incident beam 108 from a source 106. In the illustrated embodiment, the optical metrology system 100 directs the incident beam 108 onto the grating 102 at an angle of incidence θi with respect to a normal of the grating 102 and an azimuth angle φ (e.g., the angle between the plane of incidence beam 108 and the direction of the periodicity of the grating 102). A diffracted beam 110 leaves at an angle θd with respect to the normal and is received by the detector 112. The detector 112 converts the diffracted beam 110 into a measured metrology signal including spectral information. To determine the profile of the grating 102, the optical metrology system 100 includes a processing module 114 configured to receive the measured metrology signal and analyze the measured metrology signal.
Analysis of measured metrology signal generally involves comparing the measured sample spectral information to simulated spectral information to deduce a scatterometry model's parameter values that best describe the measured sample. The simulated spectral information is generally based on a solution to Maxwell's equations. Existing methods of solving Maxwell's equations typically involve rigorous coupled-wave analysis (RCWA) using Fourier analysis. RCWA using Fourier analysis involves transforming functions from the spatial domain to the spectral domain, and solving functions in the spectral domain. Models using Fourier analysis can have the advantage of being implementable without specialist knowledge of numerical method. However, existing RCWA methods make an assumption that the structure being analyzed is periodic. Furthermore, computing spectral information with existing methods can be very time-consuming and resource-intensive. Thus, computations using existing methods can inhibit providing measurements in a sufficiently timely manner for use in some applications such as semiconductor manufacturing.